A New Jersey State Police source told CNN the pilot radioed to air traffic controllers that he had experienced a bird strike and declared an emergency.

"We knew there wasn't a lot of time because we were quite close to the ground, and it felt as though the descent was somewhat rapid," said Berretta, who said he was sitting in seat 16A. Watch Berretta describe the landing »

As the plane headed down toward the river, the cabin was mostly silent, he said.

"After he told us prepare for impact, it was pretty evident we were not going to make the runway."

At first, it felt like the plane was gliding, Berretta said, as if no engines were working.

"But there was a couple of people who kind of took charge and just started yelling to calm down, just to get everybody out," he said. "Once people realized that we were going to be OK, everybody kind of calmed down and just tried to get out of the plane to safety."

Passengers began to group themselves on the wings to stay out of the frigid water.

When they were safely out of the plane, Berretta said, there was one more moment of fear.

"Our raft was tethered to the plane, and we worried we might go down with the plane," he said. "But we were able to get a knife off a rescue boat and cut the tether."

More than anything, passengers wanted to thank the crew. As Berretta exited the plane, he said that besides a few passengers remaining, the crew and pilot stayed behind to make sure everyone was out.

"I think the pilot, he did a great job," Berretta said. "I think it was as good of a landing as you can make in a river."